Abstract
This article presents a new method for closing infinite systems of equations for Green's functions. Its basis is a procedure for simultaneously splitting two higher-order Green's functions. There is a particular relationship between the three Green's functions that result. These Green's functions are self-consistent. Known Green's functions are used to reconstruct the corresponding correlation functions. An example is provided by the problem of magnetization for a spin system in the Heisenberg model with first-and secondorder approximations in the spin-spin interaction. The first-order approximation corresponds to the molecular-field approximation. The second-order computation corresponds to obtaining general relations determining the magnetization of a system.
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